We review Event Enhanced Quantum Theory (EEQT), discuss applications of EEQT to tunnelling time, and compare its quantitative predictions with other approaches, in particular with phase time and the Buttiker-Larmor approach. We discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, nonlinear, iterated function system-type, patterns arising from quantum jumps and from the associated Markov operator.